'Total return is the amount of value an investor earns from a security over a specific period, typically one year, when all distributions are reinvested. Total return is expressed as a percentage of the amount invested. For example, a total return of 20% means the security increased by 20% of its original value due to a price increase, distribution of dividends (if a stock), coupons (if a bond) or capital gains (if a fund). Total return is a strong measure of an investment’s overall performance.'

Applying this definition to our asset in some examples:- Looking at the total return, or performance of 139.4% in the last 5 years of ProShares UltraPro QQQ, we see it is relatively higher, thus better in comparison to the benchmark SPY (61.3%)
- Compared with SPY (31.6%) in the period of the last 3 years, the total return, or performance of 48.4% is greater, thus better.

'The compound annual growth rate (CAGR) is a useful measure of growth over multiple time periods. It can be thought of as the growth rate that gets you from the initial investment value to the ending investment value if you assume that the investment has been compounding over the time period.'

Which means for our asset as example:- Looking at the compounded annual growth rate (CAGR) of 19.1% in the last 5 years of ProShares UltraPro QQQ, we see it is relatively larger, thus better in comparison to the benchmark SPY (10%)
- Compared with SPY (9.6%) in the period of the last 3 years, the compounded annual growth rate (CAGR) of 14.1% is higher, thus better.

'Volatility is a statistical measure of the dispersion of returns for a given security or market index. Volatility can either be measured by using the standard deviation or variance between returns from that same security or market index. Commonly, the higher the volatility, the riskier the security. In the securities markets, volatility is often associated with big swings in either direction. For example, when the stock market rises and falls more than one percent over a sustained period of time, it is called a 'volatile' market.'

Using this definition on our asset we see for example:- The volatility over 5 years of ProShares UltraPro QQQ is 74.6%, which is higher, thus worse compared to the benchmark SPY (20.8%) in the same period.
- During the last 3 years, the volatility is 83.6%, which is larger, thus worse than the value of 24% from the benchmark.

'Downside risk is the financial risk associated with losses. That is, it is the risk of the actual return being below the expected return, or the uncertainty about the magnitude of that difference. Risk measures typically quantify the downside risk, whereas the standard deviation (an example of a deviation risk measure) measures both the upside and downside risk. Specifically, downside risk in our definition is the semi-deviation, that is the standard deviation of all negative returns.'

Applying this definition to our asset in some examples:- Compared with the benchmark SPY (15.3%) in the period of the last 5 years, the downside volatility of 54.2% of ProShares UltraPro QQQ is higher, thus worse.
- Compared with SPY (17.6%) in the period of the last 3 years, the downside volatility of 61% is larger, thus worse.

'The Sharpe ratio (also known as the Sharpe index, the Sharpe measure, and the reward-to-variability ratio) is a way to examine the performance of an investment by adjusting for its risk. The ratio measures the excess return (or risk premium) per unit of deviation in an investment asset or a trading strategy, typically referred to as risk, named after William F. Sharpe.'

Using this definition on our asset we see for example:- Looking at the ratio of return and volatility (Sharpe) of 0.22 in the last 5 years of ProShares UltraPro QQQ, we see it is relatively smaller, thus worse in comparison to the benchmark SPY (0.36)
- During the last 3 years, the Sharpe Ratio is 0.14, which is smaller, thus worse than the value of 0.3 from the benchmark.

'The Sortino ratio measures the risk-adjusted return of an investment asset, portfolio, or strategy. It is a modification of the Sharpe ratio but penalizes only those returns falling below a user-specified target or required rate of return, while the Sharpe ratio penalizes both upside and downside volatility equally. Though both ratios measure an investment's risk-adjusted return, they do so in significantly different ways that will frequently lead to differing conclusions as to the true nature of the investment's return-generating efficiency. The Sortino ratio is used as a way to compare the risk-adjusted performance of programs with differing risk and return profiles. In general, risk-adjusted returns seek to normalize the risk across programs and then see which has the higher return unit per risk.'

Using this definition on our asset we see for example:- The excess return divided by the downside deviation over 5 years of ProShares UltraPro QQQ is 0.31, which is smaller, thus worse compared to the benchmark SPY (0.49) in the same period.
- Looking at downside risk / excess return profile in of 0.19 in the period of the last 3 years, we see it is relatively smaller, thus worse in comparison to SPY (0.4).

'The Ulcer Index is a technical indicator that measures downside risk, in terms of both the depth and duration of price declines. The index increases in value as the price moves farther away from a recent high and falls as the price rises to new highs. The indicator is usually calculated over a 14-day period, with the Ulcer Index showing the percentage drawdown a trader can expect from the high over that period. The greater the value of the Ulcer Index, the longer it takes for a stock to get back to the former high.'

Using this definition on our asset we see for example:- The Ulcer Ratio over 5 years of ProShares UltraPro QQQ is 28 , which is higher, thus worse compared to the benchmark SPY (7.61 ) in the same period.
- Compared with SPY (8.93 ) in the period of the last 3 years, the Downside risk index of 33 is larger, thus worse.

'A maximum drawdown is the maximum loss from a peak to a trough of a portfolio, before a new peak is attained. Maximum Drawdown is an indicator of downside risk over a specified time period. It can be used both as a stand-alone measure or as an input into other metrics such as 'Return over Maximum Drawdown' and the Calmar Ratio. Maximum Drawdown is expressed in percentage terms.'

Which means for our asset as example:- Looking at the maximum reduction from previous high of -76.3 days in the last 5 years of ProShares UltraPro QQQ, we see it is relatively lower, thus worse in comparison to the benchmark SPY (-33.7 days)
- Looking at maximum drop from peak to valley in of -76.3 days in the period of the last 3 years, we see it is relatively lower, thus worse in comparison to SPY (-33.7 days).

'The Drawdown Duration is the length of any peak to peak period, or the time between new equity highs. The Max Drawdown Duration is the worst (the maximum/longest) amount of time an investment has seen between peaks (equity highs). Many assume Max DD Duration is the length of time between new highs during which the Max DD (magnitude) occurred. But that isn’t always the case. The Max DD duration is the longest time between peaks, period. So it could be the time when the program also had its biggest peak to valley loss (and usually is, because the program needs a long time to recover from the largest loss), but it doesn’t have to be'

Applying this definition to our asset in some examples:- Compared with the benchmark SPY (185 days) in the period of the last 5 years, the maximum time in days below previous high water mark of 296 days of ProShares UltraPro QQQ is higher, thus worse.
- During the last 3 years, the maximum days under water is 214 days, which is larger, thus worse than the value of 185 days from the benchmark.

'The Average Drawdown Duration is an extension of the Maximum Drawdown. However, this metric does not explain the drawdown in dollars or percentages, rather in days, weeks, or months. The Avg Drawdown Duration is the average amount of time an investment has seen between peaks (equity highs), or in other terms the average of time under water of all drawdowns. So in contrast to the Maximum duration it does not measure only one drawdown event but calculates the average of all.'

Using this definition on our asset we see for example:- Compared with the benchmark SPY (46 days) in the period of the last 5 years, the average time in days below previous high water mark of 73 days of ProShares UltraPro QQQ is larger, thus worse.
- During the last 3 years, the average days below previous high is 52 days, which is higher, thus worse than the value of 44 days from the benchmark.

Historical returns have been extended using synthetic data.
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- Note that yearly returns do not equal the sum of monthly returns due to compounding.
- Performance results of ProShares UltraPro QQQ are hypothetical, do not account for slippage, fees or taxes, and are based on backtesting, which has many inherent limitations, some of which are described in our Terms of Use.